Integrate exp(-(x^2)) using the substitution u=tanh(x)

The question is to convert the infinity limits of the integral [tex]\int^\infty_{-\infty} e^{{-x}^2} dx[/tex] to finite limits [tex]\int^{u_a}_{u_b} g(u) du[/tex] using the substitution [tex]u = tanh(x)[/tex].

The question is to convert the infinity limits of the integral [tex]\int^\infty_{-\infty} e^{{-x}^2} dx[/tex] to finite limits [tex]\int^{u_a}_{u_b} g(u) du[/tex] using the substitution [tex]u = tanh(x)[/tex].